课程详述

COURSE SPECIFICATION

以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问，请

联系授课教师。

The course information as follows may be subject to change, either during the session because of unforeseen

circumstances, or following review of the course at the end of the session. Queries about the course should be

directed to the course instructor.

课程名称 Course Title

现代计算方法 Mordern Numerical Methods

授课院系

Originating Department

力学与航空航天工程系 Department of Mechanics and Aerospace Engineering

课程编号

Course Code

MAE323

课程学分 Credit Value

课程类别

Course Type

专业选修课 Major Elective Courses

授课学期

Semester

春季 Spring

授课语言

Teaching Language

英文 English

授课教师、所属学系、联系方

式（如属团队授课，请列明其

他授课教师）

Instructor(s), Affiliation&

Contact

（For team teaching, please list

allinstructors）

吴雷，力学与航空航天工程系 (wul@sustech.edu.cn)

Lei Wu, Department of Mechanics and Aerospace Engineering (wul@sustech.edu.cn)

实验员/助教、所属学系、联系

方式

Tutor/TA(s), Contact

To be announced

10.

选课人数限额(可不填)

Maximum Enrolment

（Optional）

11.

授课方式

Delivery Method

讲授

Lectures

习题/辅导/讨论

Tutorials

实验/实习

Lab/Practical

其它(请具体注明)

Other（Please specify）

总学时

Total

学时数

Credit Hours

12.

先修课程、其它学习要求

Pre-requisites or Other

Academic Requirements

Calculus II B（MA102C）; Linear Algebra A（MA107A）

13.

后续课程、其它学习规划

Courses for which this course

is a pre-requisite

14.

其它要求修读本课程的学系

Cross-listing Dept.

教学大纲及教学日历 SYLLABUS

15.

教学目标 Course Objectives

This course provides a fundamental introduction to numerical analysis suitable for undergraduate

students in mathematics, computer science, physical sciences, and engineering. It is assumed that the

reader is familiar with calculus and has taken a structured programming course. It covers numerous

topics including Interpolation and Polynomial Approximation, Curve Fitting, Numerical Differentiation,

Numerical Integration (of both ordinary and partial differential equations). Interesting examples

including the simulations of Chaos (e.g. butterfly effect) and Solitons (solutions of nonlinear partial

differential equations) will be covered. It is hoped that after the course students will be able to analyse

the mathematical problems and write the computer codes to solve the practical engineering problems

of interest.

16.

预达学习成果 Learning Outcomes

On completion of this course, students will be able to:

1. Find the roots of non-linear equations

2. Perform interpolation and polynomial approximation

3. Fit curves from the given (experimental) data

4. Do numerical differentiation and numerical integration

5. Solve the ordinary differential equations numerically

6. Solve the partial differential equations numerically

完成本课程后，学生将能够：

1.求解非线性方程的根；

2.能够进行插值和多项式逼近；

3.根据给定（实验）数据拟合曲线；

4.进行数值微分和数值积分；

5.数值求解常微分方程组；

6.数值求解偏微分方程组。

17.

课程内容及教学日历（如授课语言以英文为主，则课程内容介绍可以用英文；如团队教学或模块教学，教学日历须注明

主讲人）

Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if

this is a team teaching or module course.)

Section 1: Preliminary knowledge（4 credit hours）

 Review of Calculus

 Error Analysis

 Matlab preliminaries

Section 2: Non-linear equations（4 credit hours）

 Iteration method

 Bisection methods

 Newton-Raphson and Secant methods

Section 3: Numerical solution of linear equations（4 credit hours）

 Properties of Vectors and Matrices

 Triangular Factorization

 Iterative for linear systems

 Seidel and Newton’s methods

Section 4: Interpolation and polynomial approximation（4 credit hours）

 Taylor series

 Lagrange approximation

Section 5: Interpolation and polynomial approximation（4 credit hours）

 Newton polynomials

 Chebyshev polynomials

 Pade Approximations

Section 6: Curve fitting（4 credit hours）

 Least-square line

 Spline Functions

Section 7: Fourier series and trigonometric polynomials（4 credit hours）

Section 8: Numerical differentiation（4 credit hours）

 Approximating the derivative

 Numerical differential formulas

Section 9: （4 credit hours）

 Fast Fourier Transform

Section 10: Numerical integration（4 credit hours）

 Introduction to quadrature

 Composite Trapezoidal and Simpson’s rule

 Adaptative quadrature

Section 11:（4 credit hours）

 Gauss-Legendre quadrature

 Fast Fourier Transform

Section 12: Numerical solution of ordinary differential equation （4 credit hours）

 Euler's method

 Taylor-Series Method

 Runge-Kutta method

Section 13: （4 credit hours）

 Predictor-corrector method

 Systems of differential equation

Section 14: （4 credit hours）

 Boundary value problems

 Finite-difference

 Simulation of Chaos: butterfly effect etc.

Section 15: Numerical solution of partial differential equation（4 credit hours）

 Hyperbolic equations

 Parabolic equations

Section 16: （4 credit hours）

 Elliptic equations

 Fast Fourier Transform

 Nonlinear equations having soliton solutions

18.

教材及其它参考资料 Textbook and Supplementary Readings

J. Mathews and Kurtis Fink, “Numerical Methods Using MATLAB”

课程评估 ASSESSMENT

19.

评估形式

Type of

Assessment

评估时间

Time

占考试总成绩百分比

% of final

score

违纪处罚

Penalty

备注

Notes

出勤 Attendance

课堂表现

Class

Performance

小测验

Quiz

课程项目 Projects

平时作业

Assignments

期中考试

Mid-Term Test

期末考试

Final Exam

期末报告

Final

Presentation

其它（可根据需要

改写以上评估方

式）

Others (The

above may be

modified as

necessary)

20.

记分方式 GRADING SYSTEM



A. 十三级等级制 Letter Grading

 B. 二级记分制（通过/不通过） Pass/Fail Grading

课程审批 REVIEW AND APPROVAL

21.

本课程设置已经过以下责任人/委员会审议通过

This Course has been approved by the following person or committee of authority

力学与航空航天工程系教学指导委员会

The commission of teaching instruction in department of mechanics and aerospace engineering